• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.124-129
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• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.5 s.98
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• pp.160-168
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• 1999

This paper describes one method of reverse engineering that machines a free form shape without descriptive model. A portable five-axes 3D CMM was used to digitize point data from physical model. After approximation by rational B-spline curve from digitized point data of a geometric shape, a surface was constructed by the skinning method of the cross-sectional design technique. Since a surface patch was segmented by fifteen part, surface merging was also implemented to assure the surface boundary continuity. Finally, composite surface was transferred to commercial CAD/CAM system through IFES translation in order to machine the modeled geometric shape.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.192-198
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• 2001

We consider an interpolation problem with nonuniform rational B-spline curves given ordered data points. The existing approaches assume that weight for each point is available. But, it is not the case in practical applications. Schneider suggested a method which interpolates data points by automatically determining the weight of each control point. However, a drawback of Schneiders approach is that there is no guarantee of avoiding undesired poles; avoiding negative weights. Based on a quadratic programming technique, we use the weights of the control points for interpolating additional data. The weights are restricted to appropriate intervals; this guarantees the regularity of the interpolating curve. In a addition, a knot placement is proposed for pleasing interpolation. In comparison with integral B-spline interpolation, the proposed scheme leads to B-spline curves with fewer control points.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Journal for History of Mathematics
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• v.27 no.5
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• pp.329-345
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• 2014

CAGD(Computer Aided Geometric Design) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quantities of importance such as curvatures, intersection curves between two surfaces and offset surfaces. The $B\acute{e}zier$ curves, B-spline, rational $B\acute{e}zier$ curves and NURBS(Non-Uniform Rational B-Spline) are basically and widely used in CAGD. The definitions and properties of these curves are presented in this paper. And a brief history of study on the bound for derivative of rational curves in CAGD is also presented.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.20-28
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• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline(NURBS) of an approximation method. Many of NURBS intrinsic properties are introduced and much more easily understood. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper. The object of this study is to develop the surface grid generation and the grid cluster techniques capable of resolving complex flows with shock waves, expansion waves, shear layers. The knot insert method of Non-Uniform Rational B-Spline seems well worked. In addition, NURBS has been widely utilized to generate grids in the computational fluid dynamics community. Computational examples associated with practical configurations have shown the utilization of the algorithm.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.771-771
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• 1999

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.517-525
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• 2000

A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.108-111
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• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline of an approximation method. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.